In this paper we develop an algebraic framework that allows us to extend families of two-valued states on orthomodular lattices to Baer ∗semigroups. We apply this general approach to study the full class of two-valued states and the subclass of Jauch-Piron two-valued states on Baer ∗-semigroups.

Mutant 7F2 of Salmonella enterica serovar Typhimurium has a transposon inserted in the regulator gene baeR of a two-component system and showed a more-than-fourfold reduction in resistance to ceftriaxone. Complementation analysis suggested an association among the outer membrane proteins OmpW and STM3031, ceftriaxone resistance, and baeR.

Let be an artin algebra and denote by mod(() the category of nitely generated-modules. Apart from those we are also interested in-modules which are not nitely generated. These are called large. Recall that the algebra is of innnite representation type provided that mod(() has innnitely many isomorphism classes of indecomposable objects. A theorem of Auslander asserts that there exists a large i...

Let H be a Hopf algebra and A an H-simple right H-comodule algebra. It is shown that under certain hypotheses every (H,A)-Hopf module is either projective or free as an A-module and A is either a quasi-Frobenius or a semisimple ring. As an application it is proved that every weakly finite (in particular, every finite dimensional) Hopf algebra is free both as a left and a right module over its f...

To improve the application and transfer of troubleshooting skills when diagnosing faults in complex automated production units, we developed and implemented an “anchored instruction” learning module in the context of a computer based simulation environment. The effects of the instructional module were evaluated in a quasi-experimental evaluation study. During the study 42 mechatronic apprentice...

Locally direct sums [W, Definition 3.15] appeared naturally in classification results for topological rings (see, e.g.,[K2], [S1], [S2], [S3], [U1]). We give here a result (Theorem 3) for locally compact Baer rings by using of locally direct sums. 1. Conventions and definitions All topological rings are assumed associative and Hausdorff. The subring generated by a subset A of a ring R is denote...

In this paper we investigate the conditions under which a given ring is a sub-ring of a semi-simple ring. For convenience, we say that a ring A is an extension of a ring B, if B is a sub-ring of A. It is found that the existence of a semi-simple extension is equivalent to the vanishing of the extension radical, a two-sided ideal defined analogously to the ordinary radical. In Theorem II we give...

Ayache has recently proved that if R is an integrally closed domain such that each overring of R is treed, then R is a locally pseudo-valuation domain. We investigate the extent to which the analogue (in which one concludes that R is a locally pseudo-valuation ring) holds if R is generalized to a commutative ring. A positive result is obtained if R is an idealization D(+)K where D is an integra...